In general one may try to use the same formalism to describe what is required of a system (its specification) and how it can be built from smaller components (its implementation), then the theory of systems equivalences can be very helpful to prove that a particular implementation satisfies a given specification. The kind of equivalence one is interested in depends very heavily on the particular behavioural aspects one is willing to capture. The choice is particularly debated in the case of parallel systems due to the large number of properties which may be relevant for their analysis. In this paper we discuss an compare various proposed theories of equivalence for parallel or nondeterministic systems, by adapting them to a common model which underlies many proposed models of parallelism: labelled transition systems. The stress is over operational significance of the various equivalences and over the properties they preserve.